(1/X^2)-(2/X)=8

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Solution for (1/X^2)-(2/X)=8 equation: 


D( X )

X = 0

X^2 = 0

X = 0

X = 0

X^2 = 0

X^2 = 0

1*X^2 = 0 // : 1

X^2 = 0

X = 0

X in (-oo:0) U (0:+oo)

1/(X^2)-(2/X) = 8 // - 8

1/(X^2)-(2/X)-8 = 0

1/(X^2)-2*X^-1-8 = 0

X^-2-2*X^-1-8 = 0

t_1 = X^-1

1*t_1^2-2*t_1^1-8 = 0

t_1^2-2*t_1-8 = 0

DELTA = (-2)^2-(-8*1*4)

DELTA = 36

DELTA > 0

t_1 = (36^(1/2)+2)/(1*2) or t_1 = (2-36^(1/2))/(1*2)

t_1 = 4 or t_1 = -2

t_1 = -2

X^-1+2 = 0

1*X^-1 = -2 // : 1

X^-1 = -2

-1 < 0

1/(X^1) = -2 // * X^1

1 = -2*X^1 // : -2

-1/2 = X^1

X = -1/2

t_1 = 4

X^-1-4 = 0

1*X^-1 = 4 // : 1

X^-1 = 4

-1 < 0

1/(X^1) = 4 // * X^1

1 = 4*X^1 // : 4

1/4 = X^1

X = 1/4

X in { -1/2, 1/4 }

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